Presumably you have already checked that the charging system is not giving proper DC voltage at the battery (should be 13.5 to 15.3 volts with engine running, if it's 12.something then the charging system is not charging).
The next step is to check the AC output voltage of the alternator. There is a specification in the shop manual for what it's supposed to be. Also (with the engine stopped!) make sure there is infinite resistance from ground to any of the stator connections. (otherwise one of the coils is shorted to ground)
Bad AC voltage or short-to-ground -> Stator is bad.
Good AC voltage but battery not charging (and both the ground and power leads are properly connected) -> Regulator/rectifier is bad.
Make sure the regulator/rectifier is properly grounded!!